Edward,
I've just taken a thorough look at my spare tach. To respond to your most recent post:
(1) The negative end of the capacitor connects to +12 volts, the positive end to a pad on the board that does not go anywhere. This seems odd, but perhaps the cap was hooked up for some special application.
(2) The meter movement should measure about 8 ohms, if yours reads open, that's probably the problem.

I've traced out and drawn up a schematic for my tach, hopefully correctly, though I've left out the capacitor referenced above. This drawing is attached below. Component values reflect item markings, or presume compliance with international color code standards. The unknown device could be a capacitor, thermistor, or something else entirely -- I can't tell with the means at my immediate disposal.

The other thing I'm not sure about, is the transistor. I presume that MT59/A is the part number, and that MT stands for Mullard Transistor, but I can't find any data whatsoever for the device. Possibly MT59/A is a Smiths house number for some standard part.

The circuit makes sense if I assume that the transistor is a PNP germanium device, but this has not been confirmed. (It's possible the device is an SCR or UJT, but I consider this unlikely.) The pinout is also uncertain. Pin 3 must be the collector, but it's unclear whether pins 1 and 2 are emitter and base, or base and emitter, respectively. Arguments can be made for both arrangements.

Meter zero is a mechanical adjustment. Because of the uncertainties about the transistor, it is not apparent whether the potentiometer is a calibration adjustment or a sensitivity adjustment. If the latter, then tach calibration is purely mechanical as well, probably by adjusting pointer spring tension at time of manufacture.

For a large number of subtle reasons, this tach is a sophisticated and brilliant combination of mid-20th Century technologies.